Old, well-used tubes can bleed charge for days. Less each time, but i'd be discharging before handling if five minutes have passed, until you know how this particular tube performs. Remember that you may never get any arc snap or sound if the tube has a bleeder cap on it.
One prong is fine, they're both connected.
A tube is a big capacitor. Discharging is the act of bringing the aquadag outside, or black graphite coating around the back of the tube, in contact with the aquadag inside, via the anode button i.e. connecting the two plates of the capacitor. The outside coating is connected to a grounding strap, usually, and from there will be connected to the neckboard via ground wire, and this may be connected to the frame too, if the setup has one. This may or may not be connected to mains earth, depending on the setup, and in theory you don't need to unplug from the wall if the power is off, but you'd be stupid not to. You clip onto the grounding strap with one end of your lead, and connect the other end to the anode button or the wire prongs of the shatter hook on the end of the flyback lead that connects to the anode button, as you noted above.
Hmmm, magnetic tips. Magnets and CRT's are an interesting mix. Never leave a permanent magnet anywhere near your CRT unless you mean to because you're trying to manipulate the colours. Temporarily is generally fine, if you're not talking about some enormous commercial subwoofer that's going to distort the shadowmask. I'd err on the side of caution though, and use a nonmagnetic tip if you can.
The loose wire round the yoke isn't that unusual. If it's a tinned copper loop, make sure not to break it. Otherwise just tuck it out of the way so it won't contact anything.
I wouldn't clean the flyback with anything stronger than a rag with a bit of isopropyl, or just compressed air and a toothbrush. Don't bang it around either. The potting gets microscopic cracks in it with time, and you don't want to hurry the process along. You certainly don't want to risk dissolving anything, or even starting to. If the flyback is arcing it's done, and you need a new one.
There can be many causes of arcing, but cleaning is a good first step. Often, if dust around or under the anode cap is a problem the monitor will sound like frying bacon. And if it's less severe you often get a corona you can only see in the dark. Not sure what's happening with yours. Clean the dust off the tube, clean the inside of the anode cap with isopropyl on a cloth, rub a little spark-plug grease or other high-dielectric grease around the edge of the cap to help seal it, and clean around and inside the anode button. If there's any rust you want to remove it, which might mean shoving a wad of steel wool into the anode button and working it around. TBH even if there's no rust giving the shatter hook a rub with some fine sandpaper will help it make contact.
If the cleaning doesn't fix it, you really want to watch what's going on in the dark and try to pinpoint the arc.